Abstract
AbstractThis contribution is concerned with a piezoelectric shell formulation. The present shell element has four nodes and bilinear interpolation functions. The nodal degrees of freedom are displacements, rotations and the electric potential on top and bottom of the shell. A 3D–material law is incorporated. In case of bending dominated problems incompatible approximation functions of the electrical and mechanical fields cause incorrect results. This effect occurs in standard element formulations, where the mechanical and electrical degrees of freedom are approximated with lowest order interpolation functions. In order to overcome this problem a mixed multi–field variational approach is introduced. It allows for approximations of the electric field and the strains independent of the bilinear interpolation functions. A quadratic approach for the shear strains and the electric field is proposed through the shell thickness. This leads to well balanced approximation functions regarding coupling of electrical and mechanical fields. A numerical example illustrates the more precise results in contrast to standard elements. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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